Luella drew the triangle shown on a coordinate grid. To find the triangle’s area, she multiplies 12 by 2 and then multiplies the result by another number. What is the number Luella can use to complete the calculation? The triange coordiantes are,

Question

C: (8, 10)
B: (6, 4)
A: (8, 2).

Answer 1

To find the area of triangle ABC with vertices A(8, 2), B(6, 4), and C(8, 10), we can use the formula for the area of a triangle given by the vertices' coordinates:

\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

Substituting the coordinates into the formula:

• \(A(8, 2) \rightarrow (x_1, y_1) = (8, 2)\)
• \(B(6, 4) \rightarrow (x_2, y_2) = (6, 4)\)
• \(C(8, 10) \rightarrow (x_3, y_3) = (8, 10)\)

Now, we calculate:

\[ \text{Area} = \frac{1}{2} \left| 8(4 - 10) + 6(10 - 2) + 8(2 - 4) \right| \]

Calculating each term in the absolute value:

1. \(8(4 - 10) = 8 \times (-6) = -48\)
2. \(6(10 - 2) = 6 \times 8 = 48\)
3. \(8(2 - 4) = 8 \times (-2) = -16\)

Now, substituting back into the equation:

\[ \text{Area} = \frac{1}{2} \left| -48 + 48 - 16 \right| = \frac{1}{2} \left| -16 \right| = \frac{1}{2} \times 16 = 8 \]

The area of the triangle is \(8\) square units.

Given that Luella multiplies \(12\) by \(2\) and then by another number to find the area, we can see that:

\[ 12 \times 2 \times \text{(another number)} = 8 \]

Calculating what that "another number" would be:

\[ 12 \times 2 = 24 \]

To find the "another number," set it up as follows:

\[ 24 \times \text{(another number)} = 8 \]

Now, solving for "another number":

\[ \text{(another number)} = \frac{8}{24} = \frac{1}{3} \]

Thus, the number Luella can use to complete the calculation is:

\[ \boxed{\frac{1}{3}} \]

Answer 2

the test says it's wrong

Answer 3

Let's reevaluate the area calculation of triangle ABC with the vertices \( C(8, 10) \), \( B(6, 4) \), and \( A(8, 2) \) using the formula for the area of a triangle.

The formula for the area of a triangle defined by three vertices \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \) is:

\[ \text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right| \]

Assign the coordinates accordingly:

• \( A(8, 2) \Rightarrow (x_1, y_1) = (8, 2) \)
• \( B(6, 4) \Rightarrow (x_2, y_2) = (6, 4) \)
• \( C(8, 10) \Rightarrow (x_3, y_3) = (8, 10) \)

Now plug these into the formula:

\[ \text{Area} = \frac{1}{2} \left| 8(4 - 10) + 6(10 - 2) + 8(2 - 4) \right| \]

Calculating the terms step by step:

1. Calculate \(8(4 - 10)\): \[ 8 \times (-6) = -48 \]

2. Calculate \(6(10 - 2)\): \[ 6 \times 8 = 48 \]

3. Calculate \(8(2 - 4)\): \[ 8 \times (-2) = -16 \]

Now substitute these values into the area formula:

\[ \text{Area} = \frac{1}{2} \left| -48 + 48 - 16 \right| \]

Simplifying:

\[ \text{Area} = \frac{1}{2} \left| -16 \right| = \frac{1}{2} \times 16 = 8 \]

Now we see that the area is correct.

You mentioned Luella multiplies \(12\) by \(2\), which gives \(24\), and she ends up needing to complete the area calculation. If the calculated area is \(8\) as previously determined, we can set up:

\[ 12 \times 2 \times x = 8 \] \[ 24x = 8 \] \[ x = \frac{8}{24} = \frac{1}{3} \]

Thus the calculation logically leads to \( \frac{1}{3} \) again, but if the test says this is incorrect, then there may be a misunderstanding in the area calculations or the values provided initially.

Perhaps you might double-check the specified area formula or the area requirement if there's any other context that’s not currently clear regarding the triangle or the coordinates provided.

If the triangle area or the problem context differs from the details shared initially, please provide any specific insights there. Otherwise, based on the coordinates analyzed, the consistent interpretation suggests \( \boxed{\frac{1}{3}} \).

Answer 4

luella multiple 1/2 by 2 by what to find the triangle's area?

Answer 5

Let's clarify how to express the area of triangle ABC using the given method that Luella seems to be applying.

We have already established that the area of triangle ABC, with vertices \( A(8, 2) \), \( B(6, 4) \), and \( C(8, 10) \), is \(8\) square units.

If Luella is calculating the area by multiplying \( \frac{1}{2} \) by \( 2 \) and then by some number to find the area, we can represent her area calculation as follows:

Let \( x \) be the number she needs to multiply by:

\[ \text{Area} = \frac{1}{2} \times 2 \times x \]

We know the area is \(8\), so:

\[ \frac{1}{2} \times 2 \times x = 8 \]

Calculating \( \frac{1}{2} \times 2 \):

\[ 1 \times x = 8 \]

Thus, we can solve for \( x \):

\[ x = 8 \]

So the number Luella can use to complete the calculation is:

\[ \boxed{8} \]